1. Field of the Invention
This invention relates generally to powered, concrete screeding equipment for treating concrete surfaces, including vibrating screeds. More particularly, our invention relates to a system for maximizing the mechanical power inputted to freshly placed concrete by screeding machines.
2. Description of the Prior Art
The prior art includes a vast number of differently-configured screeds and strike-offs comprising elongated spans of metal that directly contact freshly poured concrete. Relatively large and heavy duty triangular truss screeds are also well known. Typical triangular truss screeds ride upon forms, being drawn by cables and winch assemblies. Smaller, simpler screeds, including strike-offs, bull-floats and various floating screeds that are manually pushed and/or pulled by operators, are also well known. Vibration systems, which may comprise various shaft driven arrangements, or multiple, separately-powered units, comprising, for example, pneumatic vibrators, are preferred. Vigorous vibrational forces developed and distributed by finishing screeds help solidify concrete, and, importantly, water is encouraged to migrate to the surface. If vibrational screeding is optimally conducted immediately after a pour, a stronger, more chip-resistant concrete surface will result, thereby minimizing unwanted delamination. Subsequent finishing steps include troweling, which typically commences with the panning of plastic concrete. As the concrete hardens, troweling is concluded with the trowel blades after removing the pans.
U.S. Pat. No. 4,798,494 issued Jan. 17, 1989 to Allen Engineering Corporation discloses a floating, vibrating screed for striking off, float finishing and vibrating plastic concrete without being supported upon forms. A rigid, buoyant pan adapted to float upon and contact the plastic concrete includes a plurality of spaced-apart, pneumatic vibrators that vigorously vibrate the screed.
U.S. Pat. No. 4,046,484, shows a pioneer, twin rotor, self-propelled riding trowel wherein the rotors are tilted to generate steering forces. U.S. Pat. No. 3,936,212, also issued to Holz, shows a three rotor riding trowel powered by a single motor. Although the designs depicted in the above two Holz patents were pioneers in the riding trowel arts, the devices were difficult to steer and control.
Prior U.S. Pat. No. 5,108,220, owned by Allen Engineering Corporation, the same assignee as in this case, relates to an improved, fast steering system for riding trowels. It incorporates a steering system to enhance riding trowel maneuverability and control. The latter fast steering riding trowel is also the subject of U.S. Des. Pat. No. 323,510, owned by Allen Engineering Corporation.
U.S. Pat. No. 5,613,801, issued Mar. 25, 1997, to Allen Engineering Corporation, discloses a power-riding trowel equipped with separate motors for each rotor. Steering is accomplished with structure similar to that depicted in U.S. Pat. No. 5,108,220 previously discussed.
The forces exerted upon concrete by the blades or body of the chosen finishing device are many. For example, frictional forces are developed and experienced by blade contact upon the concrete surface as the trowel rotors, from which they project, forcibly revolve. Compressive forces are applied at the surface by the distributed weight of the finishing apparatus. Most importantly, a variety of forces are applied throughout the partially uncured slab by the trowel.
The amount of energy that is introduced to the concrete from the finishing equipment depends upon the intensity of the applied forces and the amount of energy that is reflected back from the concrete toward the energy source. Various physical properties of the vibrating equipment and of the concrete being finished affect the energy transmission rate and efficiency. Parameters affecting the rate of transmission and reflection of acoustic energy relate to acoustic impedance. When the acoustic impedance of the energy source substantially equals that of the energy destination, the impedances are “matched” and there is no reflection of the acoustic energy away from its destination back toward its source.
The basic method of matching acoustic impedances consists of mechanically joining a source of sound energy—a vibrator or a loudspeaker or some other source—to another object that is to be vibrated such as your eardrum or a microphone. There may in fact be several linked objects in an acoustic power train. In the most general form, there is a source of sound energy (such as a converter of electrical energy to mechanical energy, represented by the voice coil in a loudspeaker) and an absorber of sound energy (such as the load to which sound energy is applied.)
In each stage of the power train, where the form of acoustic energy is altered or where the medium in which the energy travels is changed, there exists an interface through which the energy moves. This discussion assumes that the interface is an abrupt change in nature, but it may actually be a continuous transition having a gradually changing nature. It is the impedance variation at each interface that determines the nature of energy transmission.
The energy at each interface will undergo some combination of transmission (passing through it) and reflection (reflection from it), depending upon the impedance relationship. When sound impinges on an interface where the direction of propagation is at an angle to the interface, the sound may also be bent (refracted), but in this discussion we are only considering cases where the direction of propagation is normal to (perpendicular to) the interface.
The transmission coefficient, the fraction of the energy that is transmitted through the interface, isT=(4Z1*Z2)/(Z1+Z2)2 where Z1 and Z2 are the acoustic impedances before and after the interface. Conservation of energy requires that the sum of the reflected energy and the transmitted energy totals the incident energy; there is no loss within the interface, which is a dimensionless surface rather than a physical object. The reflection coefficient, the fraction of the energy that is reflected from the interface, is 1−T.
It is not readily apparent that the transfer of energy from a concrete finishing tool (screed, float, etc.) to the concrete being finished, involves acoustic processes. It is not enough to say “it makes a noise”—although it does. The noise itself is certainly acoustic in nature. The fundamental factor is that there is a transfer of energy. If there were none, then finishing steps such as vibrational screeding would have no finishing effect and it would have no lasting influence on the concrete.
The frequency distribution of the vibrational energy applied by typical finishing machines of the character described is concentrated within relatively narrow bands of acoustic frequencies. As will be recognized by those with skill in the acoustic arts and/or familiarity with wave transmission theory in physics, the concrete masses being vibrated have a characteristic acoustic impedance. Further, the finishing machinery involved exhibits a characterized acoustic “output impedance.” Those with skill in the art of physics will appreciate the fact that, in general, the energy transfer between a given “source” and a given “load” will be optimal when the impedance of the load is approximately the same as the impedance of the source. This general principle finds examples in radio antenna theory, acoustic audio applications, and in kinetics of moving systems. We have postulated and experimentally confirmed that the vibrational energy transferred into a concrete slab by a given finishing machine will be maximized when and if the load impedance that the machine experiences is approximately the same as the machine output impedance.
Stated another way, energy transfer will be maximum when there is a minimal acoustic “standing wave ratio” (i.e., “SWR.”), which ideally should approach 1:1. Typically however, with prior art concrete finishing devices known to us, there is an appreciable mismatch between the acoustic load impedance characterizing the concrete slab, and the acoustic output impedance exhibited by the finishing machine. As the realized SWR greatly exceeds 1:1, energy that could otherwise be imparted into the concrete “load” is instead “reflected” back into the machine, unnecessarily shaking its structure and in the case of riding trowels, the machine operator. Since acoustic energy is transferred in the process, it is natural to look at the acoustic impedances of the interfaces. Concrete has characteristic impedance values which change as the concrete changes—sets and cures. Values of impedance for a typical unvibrated concrete as it ages are tabulated below:
TABLE 1Concrete Impedance At Time After Initial Placement234610Condition:Freshhourhourhourhourhour4 dayCuredImpedance:2.72.82.34.06.08.010.012.0
One possibility for our method is the use of an impedance matching insert, or transmission plate. Considering the simplified case where energy is assumed to be transmitted into the concrete in a direction normal to the surface being finished, two conditions are required to approach 100% transmission of the energy into the concrete (i.e., an acoustic SWR of 1:1). In general, the required characteristic impedance Zo of a quarter wave matching section applied between a source impedance, Zs and a load ZR is governed by the relationship:Zo2=(Zs2*ZR2).
The specific acoustic impedance of the transmission plate is the square root of that of the source and destination layers:ΔIIcII=(ΔIcII*ΔIIIcIII)1/2.
where Δ is the material density, c is the speed of sound in the material, and I, II and III refer to the source layer, the transmission plate, and the destination layer respectively. Using the physical properties given in the table below, and assuming that the energy source is made of steel, the transmission plate must have an impedance of about 10.8×106N-s/m3.
TABLE 2Selected Acoustic PropertiesSpeed of soundAcoustic ImpedanceMaterial(m/sec)Density (kg/m3)(Ns/m3 × 106)fresh concrete100025002.5Magnesium5800174010.1steel5900786046.4Granite3950275010.9
A second condition is thought to be that the thickness of the transmission plate equals one-quarter wavelength of the transmitted sound. Although the vibrational energy extends across a spectral band of frequencies, because of phenomena called “resonance”, maximal energy will be concentrated in a relatively dominant frequency. When the frequency of operation is fixed by an active transmitter or by a frequency-selective aspect of the system, design is simple; at other times, a resonant condition may determine the operating frequency. More generally, a combination of circumstances will set a range of frequencies. Testing of the equipment will provide design information. If there are no other frequency-determining factors, selection of a transmission plate thickness will force the system to operate at the condition of maximum transmission power based on the same quarter-wavelength criterion. Then, thickness selection will result in setting a resultant frequency that maximizes transmitted power.
For example, if power is to be provided to a four-inch thickness of concrete then it will be most effective when the frequency of operation corresponds to that thickness representing a quarter-wavelength of the sound energy. Fresh concrete has a sound speed of close to 1000 meters per second, so a quarter wavelength of four inches (0.1 meters) occurs at 2500 Hz. The transmission plate then will have an optimum thickness of:
TABLE 3Suggested Transmission Plate ThicknessMaterial:Suggested Thickness:Magnesium22.8 inchesGranite15.6 inches
Neither of these thicknesses are practical for concrete finishing equipment, but they illustrate what is theoretically possible.
It is also possible to match acoustic impedance by fabricating an impedance transmission plate made from two different materials, with each material having an acoustic impedance equal to one of the two terminating impedances. For a steel-to-fresh-concrete transition, one material would require an impedance of 2.5 (perhaps beechwood where it is 2.51) and the other would be made of steel. The two pieces, one made from each material, are simply glued together. The preferred system provides a means wherein the characteristic acoustic impedance of a finishing machine is matched to the acoustic impedance of the concrete load.
Tables 4 and 5 show the resultant transmission coefficients for the tabulated concrete impedances during the setting and curing cycle given on the previous page. The energy transfer characteristics are given for likely screed blade materials and for some possible plastic and wood materials that may have more favorable properties.
TABLE 4Interface Transmission Coefficient: Common MetalsFraction TransmittedAge-hoursMAGNESIUMALUMINUMTITANIUMBRASSSTEEL10.680.480.340.240.2120.690.490.350.250.2230.710.500.360.260.2340.570.390.270.190.1750.730.530.380.270.2460.810.610.450.330.2970.890.700.530.390.3580.940.760.600.450.4190.970.820.650.500.46100.990.860.710.550.50
TABLE 5Interface Transmission Coefficient: Common Plastics & WoodsplasticsAge-Fraction TransmittedTEF-hoursPINELDPEFIRHDPEBEECHUHMWLONPVC10.940.960.980.991.001.001.000.9920.930.960.970.990.991.001.001.0030.920.950.970.980.991.001.001.0040.991.001.001.000.990.980.970.9550.910.940.960.970.980.991.001.0060.840.870.900.930.950.960.980.9970.760.800.830.860.890.910.940.9680.690.730.770.800.830.860.890.9290.630.670.710.740.780.800.840.87100.580.620.660.690.730.750.790.83
When mechanical energy is generated at the interface between the vibration source and the concrete surface, it can be transmitted into the body of the concrete to the degree that the transmission coefficient (T) permits. As seen above, several materials have T quite close to 1 while the concrete is fairly fluid; in this case, up to about four hours after the pour. Specifically, HDPE (high-density polyethylene), beech wood and UHMW (ultra-high molecular weight polyethylene) have excellent transmission of acoustic energy into concrete up to the point where transfer of water and fines from the concrete interior is complete. These materials, especially UHMW since it has adequate abrasion resistance, will make excellent screed or strike-off matching systems. Under slurry-abrasion tests, UHMW is five times more abrasion resistant than steel; performance under troweling conditions has been proven substantially similar.
When concrete has hardened and water and fines have been adequately removed, the impedance of the concrete increases to the point where the transmission coefficient is too low. The energy applied to the concrete interface is no longer absorbed into the body of the concrete. It is not completely clear what the actual mechanism is, and where the acoustic energy goes, but it seems likely that it is trapped at the interface and that most of the energy is converted to heat. The observed results on the concrete surface-hardening, sealing the surface, and development of an impermeable shiny coating, is consistent with what might be expected from interfacial heating and friction.
Magnesium exhibits favorable characteristics. From 75% to almost 100% of the interfacial energy is passed into the concrete with this metal. In comparison, steel only permits 25% to 50% of the energy to pass into the concrete-a good explanation of why steel causes sealing of the concrete surface and the entrapment of water inside it. However, magnesium is not as advantageous for optimizing acoustic energy transfer as wood or plastic.